An electricity and magnetism problem by Hima Sadek
Electricity and Magnetism
Level
4
Find the current flowing in each branch of this circuit.
I1 =3.21 ,I2 =9.58 and I3 =6.21
I1 = 4.57, I2 =13.7 and I3 =1.05
I1=2.14 ,I2=10.25 and I3=0.75
I1 =1.27, I2 =8.17 and I3 =4.55
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1 solution
looking at the answers choice i figured, this question should be about finding the current in each loop not the branch current(remember these two are not the same).
Coming to the solution : In this kind of problem, mesh analysis will be lot easier.
using KVL write the equations for loop1(from left to right) as--
10 * i1 + 20 * (i1-i2) + 1000 + 30 * i1 - 1000 = 0
which on rearranging comes down to --
i2 = 3 * i1 -------------------------------------------------------eq-1.
similarly, KVL for second loop:
15 * i2 + 5 * (i2-i3) + 2000 + 40 * i2 - 1000 + 20 * (i2-i1) = 0
which on rearranging comes down to
-20 * i1+80 * i2-5 * i3 = 1000;-----------------------------------eq-2
similarly, KVL for 3rd loop:
25 * i3 + 35 * i3 + 2000 - 2000 + 5 * (i3-i2) = 0
which comes down to--
i2 = 13 * i3;----------------------------------------------------eq-3
on solving these 3 equations you can get the value of i1, i2 and i3 as 4.57A, 13.7A and 1.05A.